Problem: Chubby Yang is studying linear equations right now. He came up with a nice problem. In the problem you are given an n × n matrix W, consisting of integers, and you should find two n × n matrices A and B, all the following conditions must hold: 

  * Aij = Aji, for all i, j (1 ≤ i, j ≤ n); 
  * Bij = - Bji, for all i, j (1 ≤ i, j ≤ n); 
  * Wij = Aij + Bij, for all i, j (1 ≤ i, j ≤ n). 



Can you solve the problem?

Input

The first line contains an integer n (1 ≤ n ≤ 170). Each of the following n lines contains n integers. The j-th integer in the i-th line is Wij (0 ≤ |Wij| < 1717).

Output

The first n lines must contain matrix A. The next n lines must contain matrix B. Print the matrices in the format equal to format of matrix W in input. It is guaranteed that the answer exists. If there are multiple answers, you are allowed to print any of them.

The answer will be considered correct if the absolute or relative error doesn't exceed 10 - 4.

Examples

Input

2
1 4
3 2


Output

1.00000000 3.50000000
3.50000000 2.00000000
0.00000000 0.50000000
-0.50000000 0.00000000


Input

3
1 2 3
4 5 6
7 8 9


Output

1.00000000 3.00000000 5.00000000
3.00000000 5.00000000 7.00000000
5.00000000 7.00000000 9.00000000
0.00000000 -1.00000000 -2.00000000
1.00000000 0.00000000 -1.00000000
2.00000000 1.00000000 0.00000000

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class BSolver {
  private static InputReader in;
  private static PrintWriter out;

  public static void main(String[] args) throws IOException {
    InputStream is = System.in;
    PrintWriter pw = new PrintWriter(System.out);
    init(is, pw);
    solve();
    is.close();
    out.close();
  }

  public static void init(InputStream is, PrintWriter pw) {
    in = new InputReader(is);
    out = pw;
  }

  public static void solve() {
    int n = in.ni();
    double[][] W = new double[n][n];
    double[][] A = new double[n][n];
    double[][] B = new double[n][n];

    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
        W[i][j] = in.ni();
      }
    }

    for (int i = 1; i < n; i++) {
      for (int j = 0; j < i; j++) {
        A[i][j] = (W[i][j] + W[j][i]) / 2;
        A[j][i] = A[i][j];
        B[i][j] = W[i][j] - A[i][j];
        B[j][i] = -1 * B[i][j];
      }
    }

    for (int i = 0; i < n; i++) {
      A[i][i] = W[i][i];
    }

    String AStr = getMatrixStr(A);
    String BStr = getMatrixStr(B);

    out.println(AStr + BStr);
  }

  static String getMatrixStr(double[][] matrix) {
    StringBuilder sb = new StringBuilder();

    for (int i = 0; i < matrix.length; i++) {
      for (int j = 0; j < matrix[i].length; j++) {
        sb.append(matrix[i][j] + " ");
      }
      sb.append("\n");
    }

    return sb.toString();
  }

  private static class InputReader {
    BufferedReader br;
    StringTokenizer st;

    InputReader(InputStream stream) {
      br = new BufferedReader(new InputStreamReader(stream));
    }

    String next() {
      while (st == null || !st.hasMoreElements()) {
        try {
          st = new StringTokenizer(br.readLine());
        } catch (IOException e) {
          e.printStackTrace();
        }
      }
      return st.nextToken();
    }

    int ni() {
      return Integer.parseInt(next());
    }

    long nl() {
      return Long.parseLong(next());
    }

    int[] na(int n) {
      int[] arr = new int[n];
      for (int i = 0; i < n; i++) {
        arr[i] = ni();
      }
      return arr;
    }
  }
}